Regarding an internal combustion engine provided with a plurality of cylinders, introducing air into an intake pipe extending from a throttle valve to an intake valve through the throttle valve in exactly a throttle valve air passage amount, and discharging air from the intake pipe through an intake valve in exactly a cylinder air filling amount to fill a cylinder at the time of an intake stroke, known in the art is a control system of an internal combustion engine wherein a formula obtained from the Law of the Conservation of Mass for the intake pipe and a state equation for the air in the intake pipe is used to calculate the cylinder air filling amount of the cylinder (see Japanese Patent Publication (A) No. 2002-70633).
To use the above formula to calculate a cylinder air filling amount, for example, the temperature of the air in the intake pipe and the volume of the intake pipe have to be found. However, to find the air temperature, for example, not only is a temperature sensor necessary, but also, if considering the response delay, even if using a temperature sensor, it would be difficult to accurately find the air temperature. Further, the intake pipe includes manufacturing error, so the volume of the intake pipe cannot be considered equivalent to, for example, the design value. Measurement of the volume for each intake pipe is also extremely impractical.
Further, when using a formula to estimate a cylinder air filling amount, if using a formula obtained based on the Law of the Conservation of Mass and state equation as it is, the formula would become complicated and the calculation load would become huge, so normally this formula is simplified for use. Here, if the intake valve opening/closing timing is set to the retarded side, an intake valve will remain open even after intake bottom dead center. In this case, even if the piston starts to rise, since the intake valve is held in the open state, the air sucked into the cylinder is liable to flow back into the intake pipe. However, if simplifying the formula for use when estimating the cylinder air filling amount as explained above, this backflow of air is not considered and therefore the calculated cylinder air filling amount ends up including error.